On Non-additive Probabilistic Inequalities of Hölder-type
- 97 Downloads
Non-additive measure is a generalization of additive probability measure. Integral inequalities play important roles in classical probability and measure theory. Some well-known inequalities such as the Minkowski inequality and the Hölder inequality play important roles not only in the theoretical area but also in application. Non-additive integrals are useful tools in several theoretical and applied statistics which have been built on non-additive measure. For instance, in decision theory and applied statistics, the use of the non-additive integrals can be envisaged from two points of view: decision under uncertainty and multi-criteria decision-making. In fact, the non-additive integrals provide useful tools in many problems in engineering and social choice where the aggregation of data is required. In this paper, Hölder and Minkowski type inequalities for semi(co)normed non-additive integrals are discussed. The main results of this paper generalize some previous results obtained by the authors.
Mathematics Subject Classification (2000)Primary 99Z99 Secondary 00A00
KeywordsNonadditive measure seminormed non-additive integral semiconormed non-additive integral Chebyshev’s inequality Minkowski’s inequality Hölder’s inequality Comonotone functions
Unable to display preview. Download preview PDF.
- 7.Dubois, D., Marichal, J.-L., Prade, H., Roubens, M., Sabbadin, R.: Qualitative decision theory with Sugeno integrals. In: Proceedings of UAI’98, pp. 121–128. (1998)Google Scholar
- 13.Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. In: Trends in Logic Studia Logica Library, vol. 8, Kluwer, Dodrecht (2000)Google Scholar
- 28.Sugeno, M.: Theory of fuzzy integrals and its applications. PhD Dissertation, Tokyo Institute of Technology (1974)Google Scholar
- 33.Zhao R.: (N) fuzzy integral. J. Math. Res. Exposition 2, 55–72 (1981) (in Chinese)Google Scholar